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A certain musical scale has has 13 notes, each having a [#permalink]
 01 Jan 2004, 23:34
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A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second? A. 440 * sqrt 2 B. 440 * sqrt (2^7) C. 440 * sqrt (2^12) D. 440 * the twelfth root of (2^7) E. 440 * the seventh root of (2^12)
Last edited by Bunuel on 22 Feb 2013, 06:01, edited 1 time in total.
Edited the question and added OA.
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Re: OG PS #434-- musical scale [#permalink]
02 Jan 2004, 02:49
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stoolfi wrote:
On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to
the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2
B. 440 * sqrt (2^7)
C. 440 * sqrt (2^12)
D. 440 * the twelfth root of (2^7)
E. 440 * the seventh root of (2^12)
let the constant be k
F1 = 440
F2 = 440k
F3 = 440 k * k = 440 * k^2
F13= 440 * k^12
we know F13 = 2 *F1 = 2 * 440 = 880
880/440 = k^12
k = twelfth root of 2
for F7...
F7 = 440 * k^6 ( as we wrote for F2 and F3)
F7 = 440 * (twelfth root of 2) ^ 6
F7 = 440 * sqrt (2)
Answer A
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I agree Stoolfi, one of those wacky questions that involve figuring out the hidden "trick". The GMAT and its bag of tricks! 
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Re: OG PS #434-- musical scale [#permalink]
09 Nov 2011, 04:00
Praetorian wrote: stoolfi wrote:
On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to
the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2
B. 440 * sqrt (2^7)
C. 440 * sqrt (2^12)
D. 440 * the twelfth root of (2^7)
E. 440 * the seventh root of (2^12)
let the constant be k F1 = 440 F2 = 440k F3 = 440 k * k = 440 * k^2 F13= 440 * k^12 we know F13 = 2 *F1 = 2 * 440 = 880 880/440 = k^12 k = twelfth root of 2 for F7... F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6 F7 = 440 * sqrt (2) Answer A The question stem says that : the ratio of frequency to next higer frequency is fixed constant ... Doesnt that mean F1/F2 = k F2/F3 = k^2 and something like that .....???and not F2/F1 = k which is F2 = kF1??? 
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Re: On another thread, someone with a very good GMAT score said [#permalink]
09 Nov 2011, 22:27
Siddhans, It says the ratio of a frequency to the next higher frequency is a constant. f2/f1=f3/f2=f4/f3=.....=fixed number. This is an example of a geometric progression. Here is a video explanation: http://www.gmatquantum.com/og10-journal ... ition.htmlDabral
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Re: OG PS #434-- musical scale [#permalink]
22 Feb 2013, 04:38
Praetorian wrote: stoolfi wrote:
On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to
the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2
B. 440 * sqrt (2^7)
C. 440 * sqrt (2^12)
D. 440 * the twelfth root of (2^7)
E. 440 * the seventh root of (2^12)
let the constant be k F1 = 440 F2 = 440k F3 = 440 k * k = 440 * k^2 F13= 440 * k^12 we know F13 = 2 *F1 = 2 * 440 = 880 880/440 = k^12 k = twelfth root of 2 for F7... F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6 F7 = 440 * sqrt (2) Answer A Why do you multiply and not add? Like 1. 440 2. 440 + k and so on?
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Re: A certain musical scale has has 13 notes, each having a [#permalink]
22 Feb 2013, 05:48
Lowest frequency = 440 Highest frequency = 880 Lowest frequency (n) ^12 = Highest frequency N^12 = 2 ---------------- 1 7th note = Lowest Frequency x (n)^6 7th note = 440 x (2)^6/12 Hence the answer is A
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Re: OG PS #434-- musical scale [#permalink]
22 Feb 2013, 06:12
karmapatell wrote: Praetorian wrote: stoolfi wrote:
On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to
the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2
B. 440 * sqrt (2^7)
C. 440 * sqrt (2^12)
D. 440 * the twelfth root of (2^7)
E. 440 * the seventh root of (2^12)
let the constant be k F1 = 440 F2 = 440k F3 = 440 k * k = 440 * k^2 F13= 440 * k^12 we know F13 = 2 *F1 = 2 * 440 = 880 880/440 = k^12 k = twelfth root of 2 for F7... F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6 F7 = 440 * sqrt (2) Answer A Why do you multiply and not add? Like 1. 440 2. 440 + k and so on? Because we are given that the ratio of a frequency to the next higher frequency is a fixed constant: F2/F1=k.
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Re: OG PS #434-- musical scale [#permalink]
22 Feb 2013, 10:29
karmapatell wrote: Praetorian wrote: stoolfi wrote:
On another thread, someone with a very good GMAT score said he couldn't really understand this question. It is posted for your perusal:
A certain musical scale has has 13 notes, each having a different frequency, measured in cycles per second. In the scale, the notes are ordered by increasing frequency, and the highest frequency is twice the lowest. For each of the 12 lower frequencies, the ratio of a frequency to
the next higher frequency is a fixed constant. If the lowest frequency is 440 cycles per second, then the frequency of the 7th note in the scale is how many cycles per second?
A. 440 * sqrt 2
B. 440 * sqrt (2^7)
C. 440 * sqrt (2^12)
D. 440 * the twelfth root of (2^7)
E. 440 * the seventh root of (2^12)
let the constant be k F1 = 440 F2 = 440k F3 = 440 k * k = 440 * k^2 F13= 440 * k^12 we know F13 = 2 *F1 = 2 * 440 = 880 880/440 = k^12 k = twelfth root of 2 for F7... F7 = 440 * k^6 ( as we wrote for F2 and F3) F7 = 440 * (twelfth root of 2) ^ 6 F7 = 440 * sqrt (2) Answer A Why do you multiply and not add? Like 1. 440 2. 440 + k and so on? "For each of the 12 lower frequencies, the ratio of a frequency to the next higher frequency is a fixed constant" The question says that the ratio of two consecutive frequencies is constant. Hence we multiply.
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The Princeton Review,
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080 - 3089 2800
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Re: A certain musical scale has has 13 notes, each having a [#permalink]
22 Feb 2013, 13:59
Shoudln't "the ratio of a frequency to the next higher frequency is a fixed constant" be interpreted as f1/f2 = k instead of f2/f1=k?
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Re: A certain musical scale has has 13 notes, each having a [#permalink]
22 Feb 2013, 22:51
Let's take a simple example Series : 2 4 6 8 Now going forward the multiplying factor is 2 and backward the factor is 1/2 Hence if you go backwards in the question the factor will be 1/2 and still you will get the same answer. Posted from my mobile device 
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Re: A certain musical scale has has 13 notes, each having a
[#permalink]
22 Feb 2013, 22:51
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